Method of producing plasma by multiple-phase alternating or pulsed electrical current

ABSTRACT

A method of producing a plasma is provided. The method includes providing at least three hollow cathodes, including a first hollow cathode, a second hollow cathode, and a third hollow cathode. Each hollow cathode has a plasma exit region. The method further includes providing a source of power capable of producing multiple output waves, including a first output wave, a second output wave, and a third output wave. The first output wave and the second output wave are out of phase, the second output wave and the third output wave are out of phase, and the first output wave and the third output wave are out of phase. Each hollow cathode is electrically connected to the source of power such that the first hollow cathode is electrically connected to the first output wave, the second hollow cathode is electrically connected to the second output wave, and the third hollow cathode is electrically connected to the third output wave. Electrical current flows between the at least three hollow cathodes that are out of electrical phase. A plasma is generated between the hollow cathodes.

BACKGROUND OF THE INVENTION

Hollow cathode plasma sources are commonly used in the art for coatingand surface treatment applications. These plasma sources comprise one ormore hollow cathodes electrically connected to a source of power.Several different types of hollow cathodes may be used in these plasmasources, including point sources or linear hollow cathodes.

Power sources used in hollow cathode plasma sources are typicallyconfigured to supply one of direct current, alternating current, orpulsed current (i.e., current having a square or rectangular waveformwhere the duty cycle is less than 100%) to the hollow cathodes. Bipolarpower sources (i.e. two phase power supplies) are currently used toprovide alternating or pulsed current to a hollow cathode plasma source.

The use of direct current during operation of a linear hollow cathodeplasma source causes plasma to be generated primarily in a single area,rather than throughout the entire length of the linear hollow cathode.Although some types of plasma sources using direct current caneffectively utilize magnets to generate a uniform plasma, this cannot bedone with linear hollow cathodes. However, a high degree of uniformity(not achievable by the use of direct current in a linear hollow cathodeplasma source) is necessary for many applications, such as coating glassusing plasma-enhanced chemical vapor deposition.

The inventors previously discovered that, in a hollow cathode plasmasource, using two-phase (bipolar) alternating or pulsed power canachieve a uniform linear plasma. However, the use of two-phase power inhollow cathode plasma sources has some disadvantages. For example, dueto the alternation of the power, a plasma is not actively generated(i.e., there is no active electron emission) by the plasma source forsome portion of the operational time. For typical applications, thistime where plasma is not being actively generated is approximately 25%of a period of the power supply. Another disadvantage is that there issignificant wear on the plasma source due to the use of the two-phasepower source, which decreases the operational life of the plasma source.

Thus, there is a need in the art for plasma sources that overcome theseand other disadvantages of known plasma sources.

BRIEF SUMMARY OF THE INVENTION

The following commonly-assigned applications describe various hollowcathode plasma sources, such as may be used in embodiments of thepresent invention: U.S. application Ser. No. 12/535,447, now U.S. Pat.No. 8,652,586; U.S. application Ser. No. 14/148,612; U.S. applicationSer. No. 14/148,606; U.S. application Ser. No. 14/486,726; U.S.application Ser. No. 14/486,779; PCT/US 14/068919; PCT/US 14/68858. Eachof these applications is incorporated herein by reference in itsentirety.

Advantages of embodiments of the present invention include, but are notlimited to, improved operational life of a plasma source, improveddeposition rate, and improved time of active plasma generation.Additionally, embodiments of the present invention result in increaseddisassociation energy in the precursor gas or gasses used, which leadsto denser coatings when using plasma-enhanced chemical vapor deposition.

According to a first aspect of the invention, a plasma source isprovided. The plasma source includes at least three hollow cathodes,including a first hollow cathode, a second hollow cathode, and a thirdhollow cathode. Each hollow cathode has a plasma exit region. The plasmasource also includes a source of power capable of producing multipleoutput waves, including a first output wave, a second output wave, and athird output wave. The first output wave and the second output wave areout of phase, the second output wave and the third output wave are outof phase, and the first output wave and the third output wave are out ofphase. Each hollow cathode is electrically connected to the source ofpower such that the first hollow cathode is electrically connected tothe first output wave, the second hollow cathode is electricallyconnected to the second output wave, and the third hollow cathode iselectrically connected to the third output wave. Electric current flowsbetween the at least three hollow cathodes that are out of electricalphase. The plasma source is capable of generating a plasma between thehollow cathodes.

According to a second aspect of the invention, a method of producing aplasma is provided. The method includes providing at least three hollowcathodes, including a first hollow cathode, a second hollow cathode, anda third hollow cathode. Each hollow cathode has a plasma exit region.The method also includes providing a source of power capable ofproducing multiple output waves, including a first output wave, a secondoutput wave, and a third output wave. The first output wave and thesecond output wave are out of phase, the second output wave and thethird output wave are out of phase, and the first output wave and thethird output wave are out of phase. Each hollow cathode is electricallyconnected to the source of power such that the first hollow cathode iselectrically connected to the first output wave, the second hollowcathode is electrically connected to the second output wave, and thethird hollow cathode is electrically connected to the third output wave.Electric current flows between the at least three hollow cathodes thatare out of electrical phase. A plasma is generated between the hollowcathodes. In some embodiments, the method further includes providing asubstrate and forming a coating on the substrate using plasma-enhancedchemical vapor deposition.

In some embodiments (according to any of the aspects of the presentinvention), the plasma generated by the plasma source includes activeelectron emission for at least substantially 80% of a period of themultiple output waves; in other embodiments, the plasma source includesactive electron emission for at least substantially 90%, or at leastsubstantially 100%, of a period of the multiple output waves.

In some embodiments, the at least three hollow cathodes are out ofelectrical phase by a phase angle different from 180°. In someembodiments, the at least three hollow cathodes are out of electricalphase by a phase angle of 120°. In some embodiments, each adjacent pairof the at least three hollow cathodes is out of electrical phase by thesame phase angle as each other adjacent pair of the at least threehollow cathodes. In some embodiments, the at least three hollow cathodesare linear hollow cathodes. In some embodiments, the at least threehollow cathodes each include elongated cavities. In some embodiments,the plasma exit region for each of the at least three hollow cathodesincludes a plurality of plasma exit orifices. In some embodiments, theplasma exit region for each of the at least three hollow cathodesincludes a plasma exit slot.

In some embodiments, the at least three hollow cathodes are eachelectrically insulated such that only interior surfaces of the hollowcathode and the plasma exit region are electron-emitting and -accepting.In some embodiments, virtually all the generated plasma flows throughthe plasma exit region of each of the at least three hollow cathodes. Insome embodiments, the current flow is comprised of electrons derivedfrom secondary electron emission. In some embodiments, the current flowis comprised of electrons derived from thermionic-emitted electrons.

In some embodiments, the at least three hollow cathodes are linearlyarranged. In some embodiments, the at least three hollow cathodes areconfigured to direct each of the plasma exit regions to a common line.In some embodiments, a distance between each pair of the at least threehollow cathodes is the same distance. In some embodiments, theelectrical current flowing between the at least three hollow cathodesthat are out of electrical phase produces an electric potentialdifference (e.g., a peak-to-peak electric potential difference) betweenthe at least three hollow cathodes. In some embodiments, the electricpotential difference is at least 50V between any two of the at leastthree hollow cathodes. In some embodiments, the electric potentialdifference is at least 200V between any two of the at least three hollowcathodes. In some embodiments, the multiple output waves comprise squarewaves whereby the electric potential difference (e.g., peak-to-peakelectric potential difference) is reduced relative to sinusoidal wavesfor the same overall power input. In some embodiments, the source ofpower is in the form of AC electrical energy. In some embodiments, thesource of power is in the form of pulsed electrical energy.

In some embodiments, the generated plasma is substantially uniform overits length in the substantial absence of magnetic-field driven closedcircuit electron drift. In some embodiments, the plasma is madesubstantially uniform over its length from about 0.1 m to about 1 m. Insome embodiments, the plasma is made substantially uniform over itslength from about 1 m to about 4 m. In some embodiments, the frequenciesof each of the multiple output waves are equal and are in the range fromabout 1 kHz to about 500 MHz. In some embodiments, the frequencies ofeach of the multiple output waves are equal and are in the range fromabout 1 kHz to about 1 MHz. In some embodiments, the frequencies of eachof the multiple output waves are equal and are in the range from about10 kHz to about 200 kHz. In some embodiments, the frequencies of each ofthe multiple output waves are equal and are in the range from about 20kHz to about 100 kHz. In some embodiments, the electrons from anemitting surface are confined by the hollow cathode effect. In someembodiments, the electrons from an emitting surface of each of the atleast three hollow cathodes are not confined by magnetic fields. In someembodiments, at least one of the multiple output waves produced by thesource of power is configured to power a plurality of the at least threehollow cathodes.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and form partof the specification, illustrate various embodiments of the presentdisclosure and, together with the description, further serve to explainthe principles of the disclosure and to enable a person skilled in thepertinent art to make and use the embodiments disclosed herein. In thedrawings, like reference numbers indicate identical or functionallysimilar elements.

FIG. 1 illustrates a three-phase sinusoidal waveform according toexemplary embodiments of the present invention.

FIG. 2 illustrates voltage and current plots between a pair of hollowcathodes in a bipolar hollow cathode plasma source.

FIG. 3 illustrates a cross-sectional view of a conventional bipolarhollow cathode plasma source at different points in time.

FIG. 4 illustrates regions of plasma off-time in a conventional bipolarhollow cathode plasma source.

FIG. 5 illustrates voltage and current plots between pairs of hollowcathodes in a multiphase hollow cathode plasma source according toexemplary embodiments of the present invention.

FIG. 6 illustrates a cross-sectional view of a multiphase hollow cathodeplasma source at different points in time according to exemplaryembodiments of the present invention.

FIG. 7 illustrates a method according to exemplary embodiments of thepresent invention.

FIG. 8 illustrates a coating formed by methods according to exemplaryembodiments of the present invention.

FIG. 9 illustrates a multiphase hollow cathode plasma source includinghollow cathodes having a plasma exit region according to exemplaryembodiments of the present invention.

FIG. 10 illustrates a multiphase hollow cathode plasma source includinghollow cathodes having a slot-like, restricted plasma exit regionaccording to exemplary embodiments of the present invention.

FIG. 11 illustrates a multiphase hollow cathode plasma source includingsix hollow cathodes and six phases according to exemplary embodiments ofthe present invention.

FIG. 12 illustrates a multiphase hollow cathode plasma source includingsix hollow cathodes and three phases according to exemplary embodimentsof the present invention.

FIG. 13 illustrates a multiphase hollow cathode plasma source includingthree equidistant hollow cathodes according to exemplary embodiments ofthe present invention.

FIG. 14A illustrates electron density of the plasma formation in andaround the hollow cathodes in a bipolar hollow cathode plasma source.

FIG. 14B illustrates electron density of the plasma formation in andaround the hollow cathodes in a multiphase hollow cathode plasma sourceaccording to exemplary embodiments of the present invention.

FIG. 15A illustrates ion density of the plasma formation in and aroundthe hollow cathodes in a bipolar hollow cathode plasma source.

FIG. 15B illustrates ion density of the plasma formation in and aroundthe hollow cathodes in a multiphase hollow cathode plasma sourceaccording to exemplary embodiments of the present invention.

FIG. 16A illustrates ion absorption along the wall of a hollow cathodecavity in both a bipolar hollow cathode plasma source and a multiphasehollow cathode plasma source according to exemplary embodiments of thepresent invention.

FIG. 16B illustrates an index along a wall of a hollow cathode cavity asshown in the graph of FIG. 16A.

FIG. 17 illustrates a schematic representation of a plurality of exitorifices.

DETAILED DESCRIPTION OF THE INVENTION

Consider a sine wave A sin 2πft+φ, where A is the amplitude, f is thefrequency, and φ is the phase angle. The phase angle φ specifies wherethe oscillation is at time t=0. With respect to two sine waves A₁ sin2πft+φ₁ and A₂ sin 2πft+φ₂, the phase difference between the two wavesis defined as the difference of phase angles φ₂−φ₁. Note that thisdefinition makes the phase difference depend on which wave is consideredthe first wave and which wave is considered the second wave. That is, ifthe order is changed, the sign of the phase difference will change. Thewave that has a larger phase angle is said to be the leading wave, andthe wave with a smaller phase angle is said to be the lagging wave. Ifthe leading wave is considered to be the first wave, and the phasedifference is φ, then considering the lagging wave as the first wavewill lead to a phase difference of −φ. Generally this specification willnot treat the sign of the phase difference with much significance, andwill not consider the order of the waves as significant. Although φ isexpressed in radians in the formula above, this application willgenerally discuss (as a matter of convenience) phase angle or phasedifference in degrees. Since a sine wave has a cycle or period ofexactly 360° (or 2πradians), the phase angle φ can be expressed as anumber between −180° (or −πradians) and +180° (or +πradians). The phasedifference is independent of amplitude A and is properly defined onlybetween two waves that have the same frequency f.

Where the two waves share the same phase angle φ, there is no phasedifference and the waves are said to be in phase (with respect to eachother). Where the two waves do not share the same phase angle φ, thewaves are said to be out of phase (with respect to each other). Wherethe phase difference is 180°, the two waves are said to be antiphase(with respect to each other). Phase difference is a property between twowaves. Two waves that have a phase difference with respect to each othermay also be referred to as being offset, or phase-offset, from eachother. One of ordinary skill in the art will also recognize that phasedifference can be defined for square waves, pulse waves, and otherwaveforms.

When two hollow cathodes are being powered by two waves that are out ofphase, this application will refer to those hollow cathodes as beingphase offset (with respect to each other) by a given phase angle,defined as the phase difference of the two waves powering the hollowcathodes. Thus, either the waves or the hollow cathodes can be said(interchangeably) to be phase offset from each other. Alternatively, ifthe two waves are in phase, the two hollow cathodes will(interchangeably) be referred to as being in phase.

“Thermionic” is taken to mean electron emission from a surface whereemission is greatly accelerated by an elevated surface temperature.Thermionic temperatures are generally about 600° C. or greater.

“Secondary electron” or “secondary electron current” is taken to meanelectron emission from a solid surface as a result of bombardment ofthat surface by a particle and the current that is created as a result,respectively. Electron emitting surfaces in accordance with embodimentsof the present invention can generate a plasma and the surfaces are, inturn, further impinged upon by electrons or ions. The impingement of theelectron emitting surfaces by electrons, or ions, results in secondaryelectrons emitted from the electron emitting surfaces. Secondaryelectron emission is important because secondary electron flow aids increating a densified plasma.

FIG. 1 illustrates a three-phase sinusoidal waveform according toembodiments of the present invention. The three different sinusoidalwaves (A, B, C) in waveform plot 100 are each out of phase by ±120° withrespect to each other. Specifically, pairs (A, B) and (B, C) are eachout of phase by +120° and pair (A, C) is out of phase by −120°.

FIG. 2 illustrates voltage and current plots between a pair of hollowcathodes in a bipolar hollow cathode plasma source. Time points t₁, t₂,t₃, t₄, t₅, and t₆ are indicated on voltage plot 202 and current plot204 and denote various points of interest.

FIG. 3 illustrates a cross-sectional view of a conventional bipolarhollow cathode plasma source at different points in time. Bipolar hollowcathode arrangement 300 includes hollow cathodes 302, 304 and a bipolarpower source 310. When power is supplied by power source 310, a plasma320 is generated between hollow cathodes 302, 304. Voltage plot 202 andcurrent plot 204 indicate, respectively, the voltage and current betweenhollow cathodes 302, 304. Power source 310 provides an alternatingcurrent, and hollow cathodes 302, 304 alternately serve as cathode andanode. In this arrangement, hollow cathodes 302, 304 are in antiphase(i.e., out of phase by 180°). Time points t₁, t₂, t₃, t₄, t₅, and t₆ areindicated on voltage plot 202 and current plot 204 and denote variouspoints of interest, which correspond to the different views of hollowcathode arrangement 300 shown in FIG. 3.

The view corresponding to t₁ shows the point where the alternatingvoltage input and resulting current both reach a zero value. At thispoint, plasma is not being actively generated. The view corresponding tot₂ shows the point where the potential difference between hollowcathodes 302, 304 reaches a maximum and plasma 320 is ignited. The viewcorresponding to t₃ shows the point of maximum current, where plasma 320is fully established between the two hollow cathodes 302, 304. The viewcorresponding to t₄ shows the bipolar hollow cathode arrangement 300 ata point where current is equal to the current at t₂, where a plasma 320of diminished intensity (compared to, for example, the viewcorresponding to t₃) exists. The view corresponding to t₅ shows the nextzero crossing, where plasma generation has once again ceased. The viewcorresponding to t₆ shows the continued cycle with plasma 320 againbeing generated, and where hollow cathode 302 and hollow cathode 304have switched roles (cathode or anode) as compared to t₂.

The switching of roles between cathode and anode is briefly described.The bipolar power supply initially drives a first electron emittingsurface to a negative voltage, allowing plasma formation, while thesecond electron emitting surface is driven to a positive voltage inorder to serve as an anode for the voltage application circuit. Thisthen drives the first electron emitting surface to a positive voltageand reverses the roles of cathode and anode. As one of the electronemitting surfaces is driven negative, a discharge forms within thecorresponding cavity. The other cathode then forms an anode, causingelectron current to flow from the cathodic hollow cathode to the anodichollow cathode.

FIG. 4 illustrates regions of plasma off-time in a conventional bipolarhollow cathode plasma source. Specifically, FIG. 4 identifies theregions of time along the voltage plot 202 and current plot 204 whereinsufficient potential difference exists between the hollow cathodes foractive plasma formation. In the non-plasma-generating regions 402, 404,and 406, the bipolar hollow cathode arrangement 300 ceases to generateplasma for approximately 25% of each wave period. In contrast, anadvantage of embodiments of the present invention is that by maintainingsufficient potential difference between hollow cathodes for plasmageneration, embodiments of the present invention are capable of reducingor eliminating the period of time where there is no plasma being formed.

FIG. 5 illustrates voltage and current plots between pairs of hollowcathodes in a multiphase hollow cathode plasma source according toembodiments of the present invention. Time points t₁₀, t₁₁, t₁₂, t₁₃,t₁₄, and t₁₅ are indicated on voltage plots 502, 506, 510 and currentplots 504, 508, 512 and denote various points of interest.

FIG. 6 illustrates a cross-sectional view of a multiphase hollow cathodeplasma source at different points in time according to embodiments ofthe present invention. Multiphase hollow cathode arrangement 600includes hollow cathodes 602, 604, 606 and a multiphase power source610. When power is supplied by power source 610, a plasma 620 isgenerated between hollow cathodes 602, 604, 606. Specifically, plasma620 is generated between each pair of hollow cathodes 602, 604; 604,606; and 602, 606. Voltage plots 502, 506, 510 and current plots 504,508, 512 (as shown in FIG. 5) indicate, respectively, the voltage andcurrent between hollow cathode pairs 602, 604 (labeled “A-B” in FIG. 5);604, 606 (labeled “B-C” in FIG. 5); and 602, 606 (labeled “A-C” in FIG.5) (hollow cathode pairs as shown in FIG. 6). Power source 610 providesan alternating current, and hollow cathodes 602, 604, 606 alternatelyserve as cathode and anode. In this arrangement, hollow cathode pairs602, 604 and 604, 606 are out of phase by +120° and hollow cathode pair602, 606 is out of phase by −120°. Time points t₁₀, t₁₁, t₁₂, t₁₃, t₁₄,and t₁₅ are indicated on voltage plots 502, 506, 510 and current plots504, 508, 512 and denote various points of interest, which correspond tothe different views of hollow cathode arrangement 600 shown in FIG. 6.

The plasma generated between any pair of hollow cathodes will beaffected, in part, by the distance between the pair of hollow cathodes.In some embodiments, the distance between adjacent pairs of hollowcathodes (e.g., hollow cathode pairs 602, 604 and 604, 606) is the same,or substantially the same, while the distance between non-adjacenthollow cathodes (e.g. hollow cathodes 602, 606) is greater than thedistance between adjacent pairs. If the distance between a pair ofhollow cathodes is too large, plasma may not be formed between them. Aswill be recognized by one of skill in the art, distance between hollowcathodes is process dependent. As distance increases, the voltagerequired for plasma formation increases. In some embodiments, thedistance between hollow cathodes is less than 500 mm, or less than 400mm, or less than 200 mm. In some embodiments, the distance betweenhollow cathodes is about 100 mm. Although plasma formation can occur forlarger distances, for typical processes and power supplies, a maximumdistance might be 500 mm. Magnetic fields can also influence effectivespacing ranges.

The plasma generated will also be affected, in part, by the voltage andcurrent between the pair of hollow cathodes. For example, althoughplasma may be forming between multiple pairs of hollow cathodes, theplasma density may not be uniform, in part due to the difference involtage and current between different pairs of hollow cathodes. For usein coating a substrate using plasma-enhanced chemical vapor deposition,for example, this non-uniformity will not be substantial, because thenon-uniformities occur only during a short time span and the higher andlower plasma density areas switch many times before the substrate willhave moved appreciably. Further, for inline coating processes, becausethe substrate moves beneath the plasma source and passes under eachhollow cathode, the substrate will be equally treated.

Multiphase power source 610 may include a single power source ormultiple power sources. Specifically, multiphase power source 610 iscapable of generating multiple output waves (e.g., waves A, B, and C inwaveform plot 100), where the multiple output waves (and hence, thehollow cathodes that those waves power) are each phase-shifted from oneanother with respect to time. In some embodiments, adjacent hollowcathodes e.g. hollow cathode pairs 602, 604 and 604, 606) are each phaseshifted by the same phase angle from each other (e.g. 120° for athree-phase power source, 90° for a four-phase power source, 72° for afive-phase power source, 60° for a six phase power source,

$\frac{360{^\circ}}{n}$for an n-phase power source). For a three-phase three-hollow-cathodelinear embodiment (i.e. hollow cathodes are arranged in a line), if eachadjacent hollow cathode pair 602, 604 and 604, 606 is out of phase by120°, then non-adjacent hollow cathode pair 602, 606 would be out ofphase by −120°. For a four-phase four-hollow-cathode linear embodiment,if each adjacent pair is out of phase by 60°, then the non-adjacent pairconsisting of the first and third hollow cathodes in the line would beout of phase by 120° and the non-adjacent pair consisting of the firstand the fourth hollow cathodes in the line would be out of phase by180°.

The view corresponding to t₁₀ shows the point where current flow betweenhollow cathodes 602 and 604 is at a maximum, while current flow betweenhollow cathodes 604 and 606 is approximately half of the maximum value.In the view corresponding to t₁₁, current flow between hollow cathodes602 and 604 becomes zero while current begins flowing between hollowcathodes 602 and 606. At this same point (t₁₁), current flow betweenhollow cathodes 604 and 606 reaches its maximum value. The cyclecontinues in the view corresponding to t₁₂, when current flow betweenhollow cathodes 602 and 606 reaches a maximum value and current againbegins to flow between hollow cathodes 602 and 604, though in theopposite direction from that depicted in the view corresponding to t₁₀.The view corresponding to t₁₃ depicts the opposite end of the cycle fromthe view corresponding to t₁₀, where maximum current flows betweenhollow cathode 602 and 604, while approximately half of the maximumcurrent flows between hollow cathodes 604 and 606. The current flows ofthe view corresponding to t₁₃ are in the opposite directions of those inthe view corresponding to t₁₀, with the hollow cathodes that previouslyserved as cathodes now serving as anodes. The view corresponding to t₁₄depicts the opposite current flow situation of what was described in theview corresponding to t₁₁, and the view corresponding to t₁₅ shows theopposite current flow situation of what was described in the viewcorresponding to t₁₂.

One characteristic of the multiphase hollow cathode arrangement 600depicted in FIG. 6 (as well as in other embodiments of the presentinvention) is that at each point when current flow approaches zerobetween any two hollow cathodes, the voltage difference and current flowbetween other hollow cathode pairs is nonzero. With this arrangement, itis possible to create a plasma device which does not experience thepreviously mentioned plasma off-time of conventional plasma sourcesdriven by bipolar power. That is, embodiments of the present inventioneffectively avoid the non-plasma generating regions 402, 404, 406inherent in the prior art bipolar hollow cathode arrangement 300, asdiscussed above. By including at least three hollow cathodes and amultiphase power source, according to embodiments of the presentinvention, improved plasma characteristics may be obtained, including adevice which maintains current flow and the resultant plasma generationfor the entirety of its operational time, thereby producing continuousplasma generation. By using at least three phase-offset waves and atleast three hollow cathodes, there will be substantially no plasmaoff-time where the waves are generated by an alternating current powersource. For pulsed power, the plasma off-time may be from substantially0% to around 20%, depending on design parameters. For example, usingpulsed power with at least three phase-offset waves and at least threehollow cathodes, the plasma off-time may be substantially 20% (oralternatively, active plasma generation for 80% of a period of thewaves); the plasma off-time may be substantially 10% (or alternatively,active plasma generation for 90% of a period of the waves); the plasmaoff-time may also be substantially 0% (or alternatively, active plasmageneration for 100% of a period of the waves). Because there is a decaytime associated with plasma—i.e., even after voltage drops to zerobetween a pair of hollow cathodes, plasma may still be present for ashort time thereafter, even though it is not being activelygenerated—this application refers to active plasma generation as thetime where there is active electron emission.

In some embodiments, hollow cathodes 602, 604, 606 (or any other hollowcathode arrangement described in or enabled by this specification) mayinclude elongated cavities. The hollow cathodes may include a plasmaexit region, and the plasma exit region may include a single plasma exitorifice or a plurality of plasma exit orifices (e.g., plasma exitorifices 1701, as shown in FIG. 17) or an plasma exit slot or somecombination of these plasma exit regions. In some embodiments, thehollow cathodes are each electrically insulated such that only interiorsurfaces of the hollow cathode and the plasma exit region areelectron-emitting and -accepting. In some embodiments, virtually all thecontinuously generated plasma flows through the plasma exit region ofeach of the hollow cathodes. In some embodiments, current flow iscomprised of secondary electron emission or thermionic-emitted electronsor some combination of these current flows. In some embodiments, anelectric potential difference causes current to flow between the hollowcathodes. In some embodiments, this potential difference is at least 50Vor at least 200V between any two of the hollow cathodes. In someembodiments, the multiphase power source that produces multiple outputwaves produces multiple output waves comprised of square waves, wherebythe electric potential difference is reduced relative to sinusoidalwaves. The multiphase power source is in the form of AC electricalenergy or in the form of pulsed electrical energy or some combination ofthese forms of electrical energy. In some embodiments, the plasma thatis generated is substantially uniform over its length in the substantialabsence of magnetic-field driven closed circuit electron drift. In someembodiments, the plasma is made substantially uniform over its lengthfrom about 0.1 m to about 1 m or from about 1 m to about 4 m. In someembodiments, the frequencies of each of the multiple output waves areequal and are in the range of from about 1 kHz to about 1 MHz or fromabout 10 kHz to about 200 kHz or from about 20 kHz to about 100 kHz. Insome embodiments, the electrons emitted from an emitting surface areconfined by the hollow cathode effect. In some embodiments, theelectrons emitted from an emitting surface are not confined by magneticfields.

One factor influencing electron current is the temperature of hollowcathode cavity walls. In a hollow cathode setup with cavity walltemperature below 1000° C., electron emission is dominated by secondaryelectron emission. As cavity walls are bombarded by ions, the impactingion kinetic energy along with a negative voltage potential induceselectrons to be emitted from wall surfaces. Typically, these “cold”hollow cathodes are run with cavity wall temperatures from 50° C. to500° C. Generally, to maintain hollow cathode structures at thesetemperatures, cooling methods are applied. Often, water cooling channelsare built into the hollow cathode structure. Operating voltage for coldhollow cathode discharges is typically from 300 volts to 1000 volts.

Alternatively, hollow cathodes may be run in thermionic mode. Forthermionic electron emission to occur, hollow cathode cavity walltemperatures usually range from 1000° C. to 2000° C. Thermionic hollowcathodes may incorporate heaters around cavity walls to help raisetemperature or, more simply, may rely on plasma energy transfer to heatcavity walls. Generally, hot cavities are thermally insulated to reduceconductive or radiative heat loss. Operating voltage for thermionichollow cathode discharges is typically from 10 volts to 300 volts ormore commonly from 10 volts to 100 volts.

Commercially useful PECVD processes with sufficiently high depositionrates depend on plasmas that have undergone some method ofdensification. The hollow cathode effect is a specific method ofelectron densification and confinement making use of enclosed orpartially enclosing electric fields. Gas phase free electrons aretrapped by enclosing negative fields and exhibit oscillating movementbetween the surrounding or facing negatively biased walls. Electronoscillations result in long electron path lengths which in turn resultin high probability of gas phase collisions. These collisions ionize thegas molecules creating additional electrons and positive ions. Thepositive ions are accelerated to and collide with the negatively biasedhollow cathode walls. The positive ion-wall collisions result in furtherelectron generation through secondary electron emission. Literatureindicates hollow cathode plasmas are generally denser plasmas than thosederived from magnetic confinement such as is used in closed driftelectron confinement processes (e.g., magnetron sputtering).

Another advantage of the embodiment in FIG. 6, as well as otherembodiments of the present invention, is that by including additionalhollow cathodes a wider plasma is generated, which results in improvedPECVD deposition rate.

FIG. 7 illustrates a method according to embodiments of the presentinvention. The multiphase hollow cathode arrangement 600 (and otherhollow cathode arrangements described and enabled by this disclosure)may be used to generate a continuous plasma. A method 700 of producing aplasma includes providing at least three hollow cathodes (step 702).Each hollow cathode has a plasma exit region. The method also includesproviding a source of power capable of producing multiple output waves(step 704). Each hollow cathode is electrically connected to the sourceof power. The multiple output waves produced by the source of power areeach phase-shifted from one another with respect to time to cause eachhollow cathode to be out of electrical phase with the other hollowcathodes. Electrical current flows between the at least three hollowcathodes that are out of electrical phase. A plasma is continuouslygenerated between the hollow cathodes. In some embodiments, the methodfurther includes providing a substrate (step 706) and forming a coatingon the substrate using plasma-enhanced chemical vapor deposition (step708). The dashed boxes around steps 706 and 708 in FIG. 7 indicate thatthese steps are optional. Forming a coating on the substrate usingplasma-enhanced chemical vapor deposition (PECVD) may include providingprecursor gasses, process gasses, reactant gasses, or a combination ofthese, into the hollow cathode cavities or through manifolds adjacent tothe hollow cathodes. Those of skill in the art will recognize that othersteps applicable to PECVD may also be included.

FIG. 8 illustrates a coating formed by methods according to embodimentsof the present invention. Coating 802 is formed on top of substrate 804,creating a coating-substrate combination 800. In some embodiments,substrate 804 is glass. In other embodiments, substrate 804 may includeplastic, metal, semiconductor material, or other suitable material foruse in a PECVD process. In some embodiments, coating 802 may be a singlelayer or film or may include a plurality of layers or films. In someembodiments, coating 802 may be a low-emissivity coating and substrate804 may be a glass window, such that coating-substrate combination 800is suitable for architectural use. In some embodiments, coating 802 maybe another coating for a specific application, such as an anti-fogcoating for use in refrigerator doors or a transparent conductive oxidecoating for use in photovoltaic cells.

FIG. 9 illustrates a multiphase hollow cathode plasma source includinghollow cathodes having a plasma exit region according to embodiments ofthe present invention. Linear multiphase hollow cathode arrangement 600(shown in FIG. 9) includes hollow cathodes 602, 604, 606 and multiphasepower source 610. Each hollow cathode 602, 604, 606 is powered from themultiphase power source 610 by alternating or pulsed power such thateach hollow cathode is phase offset from one another. Each hollowcathode 602, 604, 606 includes a hollow cathode cavity 904 and plasmaoutlet 902. In the embodiment shown in FIG. 9, hollow cathodes 602, 604,606 include two spaced-apart side regions and a top region, defining thecavity 904, and an open bottom region defining the plasma outlet 902. Areactant gas (or process gas or precursor gas or a combination of thesegasses) may be present in hollow cathode cavity 904 of each hollowcathode 602, 604, 606. A reactant gas (or process gas or precursor gasor a combination of these gasses) may also be present in a reactionregion 910. In some embodiments, reaction region 910 may include asubstrate, such as substrate 804, and in some embodiments, a coating maybe formed on the substrate in reaction region 910. When power issupplied by multiphase power source 610, electrons alternately flowbetween each of the hollow cathodes 602, 604, 606, generating plasmawhich flows out of plasma outlets 902 into reaction region 910.

FIG. 10 illustrates a multiphase hollow cathode plasma source includinghollow cathodes having a slot-like, restricted plasma exit regionaccording to embodiments of the present invention. The embodiment ofFIG. 10 is an alteration of the embodiment of FIG. 9, where plasmaoutlet 902 is replaced by a slot-like plasma outlet 1002. Each hollowcathode 602, 604, 606 includes a hollow cathode cavity 904 and plasmaoutlet 1002. In the embodiment shown in FIG. 10, hollow cathodes 602,604, 606 include two spaced-apart side regions and a top region spacedapart from a bottom region, such that plasma outlet 1002 is defined by aslot in the bottom region. The plasma outlet 1002 allows for higher gaspressure inside of the hollow cathodes 602, 604, 606 when process gas isinside the hollow cathode cavity 904.

As described above, a multiphase plasma source according to embodimentsof the invention can include three hollow cathodes, each phase shiftedfrom each other, i.e. three-phase, three-hollow-cathode embodiments. Oneof skill in the art will recognize that other embodiments are possible,such as four-, five-, or six phase embodiments, and that in general, amultiphase hollow cathode arrangement can be provided for an n-phaseembodiment, where n is greater than 2. Using additional hollow cathodesand phase-shifted waves enables the creation of a plasma with thedesired characteristics for a given process or use. As the embodimentsin FIGS. 9 and 10 show (and as described below), an n-phase hollowcathode arrangement, according to embodiments of the present invention,may include m hollow cathodes, where n is less than or equal to m. For asystem with m hollow cathodes, there will be

$\begin{pmatrix}m \\2\end{pmatrix}\quad$pairs of hollow cathodes (irrespective of order). Thus, for example, toshow representative voltage and current plots analogous to those shownin FIG. 5 for a three-hollow-cathode embodiment, would require 15voltage plots and 15 current plots for

$m = {6{\left( {\begin{pmatrix}6 \\2\end{pmatrix} = 15} \right).}}$Where the hollow cathodes are arranged linearly, there will be m−1adjacent pairs of hollow cathodes. Having fewer phases which drivemultiple hollow cathodes can simplify the requirements for a multiphasepower source, and can also alter the characteristics of the plasmagenerated as a function of time, as a person of ordinary skill in theart will understand from the present disclosure.

FIG. 11 illustrates a multiphase hollow cathode plasma source includingsix hollow cathodes and six phases according to embodiments of thepresent invention. That is, in this embodiment m=6 and n=6. Multiphasehollow cathode arrangement 1100 includes hollow cathodes 1102, 1104,1106, 1108, 1110, 1112 connected to a multiphase power source 1110configured to power each hollow cathode with a separate phase-offsetwave 1120, 1122, 1124, 1126, 1128, 1130. In one embodiment, adjacenthollow cathode pairs are each phase shifted from one another by the samephase angle (e.g. by 60°). Adjacent hollow cathode pairs, as shown inFIG. 11, include hollow cathode pairs 1102, 1104; 1104, 1106; 1106,1108; 1108, 1110; and 1110, 1112. In the embodiment shown in FIG. 11,where adjacent pairs are out of phase by 60°, non-adjacent pairs 1102,1108; 1104, 1110; and 1106, 1112 are each in antiphase with respect toeach other. There are 10 non-adjacent pairs in the embodiment of FIG. 11

$\left( {{\begin{pmatrix}6 \\2\end{pmatrix} - \left( {6 - 1} \right)} = {{15 - 5} = 10}} \right).$The phase difference of each pair of hollow cathodes in FIG. 11, whereadjacent pairs are phase shifted by 60°, is shown in the table below.

TABLE 1 Pair Offset 1102, 1104 60° 1102, 1106 120° 1102, 1108 180° 1102,1110 −120° 1102, 1112 −60° 1104, 1106 60° 1104, 1108 120° 1104, 1110180° 1104, 1112 −120° 1106, 1108 60° 1106, 1110 120° 1106, 1112 180°1108, 1110 60° 1108, 1112 120° 1110, 1112 60°

FIG. 12 illustrates a multiphase hollow cathode plasma source includingsix hollow cathodes and three phases according to embodiments of thepresent invention. That is, in this embodiment, m=3 and n=6. Hollowcathode arrangement 1200 includes hollow cathodes 1102, 1104, 1106,1108, 1110, 1112 connected to multiphase power source 1210. Multiphasepower source 1210 produces three phase-offset waves 1220, 1222, 1224. Inthis embodiment, wave 1220 powers hollow cathodes 1102, 1108; wave 1222powers hollow cathodes 1104, 1110; and wave 1224 powers hollow cathodes1106, 1112. In some embodiments, each wave 1220, 1222, 1224 is offset bythe same phase angle (e.g., 120°). In the embodiment shown in FIG. 12,non-adjacent pairs 1102, 1108; 1104, 111.0; and 1106, 1112 are each inphase with respect to each other, since there is a single wave 1220,1222, 1224 powering each pair. The phase difference of each pair ofhollow cathodes in FIG. 12, where adjacent pairs are phase shifted by120°, is shown in the table below.

TABLE 2 Pair Offset 1102, 1104 120° 1102, 1106 −120° 1102, 1108 0° 1102,1110 120° 1102, 1112 −120° 1104, 1106 120° 1104, 1108 −120° 1104, 11100° 1104, 1112 120° 1106, 1108 120° 1106, 1110 −120° 1106, 1112 0° 1108,1110 120° 1108, 1112 −120° 1110, 1112 120°

FIG. 13 illustrates a multiphase hollow cathode plasma source includingthree equidistant hollow cathodes. Arrangement 1300 includes threehollow cathodes 602, 604, 606 with plasma outlets 1002 each directed toa common line (note that because FIG. 13 is a cross-sectional view, itappears that each of the outlets is directed to a common point). As willbe apparent, the embodiment shown in FIG. 13 can also include additionalhollow cathodes, in various geometric configurations, such that theplasma outlets of each of the hollow cathodes (or some subset of thehollow cathodes) are directed to a common line (or a set of commonlines). In some embodiments, the distance between each of the hollowcathodes (adjacent and non-adjacent) is equal. For example, FIG. 13shows a distance between hollow cathode pair 602, 604 beingsubstantially the same as a distance between each of hollow cathode pair602, 606 and hollow cathode pair 604, 606. In some embodiments, adistance between hollow cathode pairs may be measured from the center ofa hollow cathode, from the plasma outlet of a hollow cathode, or fromsome other point in, on, or near a hollow cathode. The embodiment ofFIG. 13, or similar embodiments, may be used, for example, to coattwo-dimensional substrates such as wire or optical fiber coating. Forexample, two-dimensional substrates may be coated uniformly by passingthese elongated substrates through the line of common direction.

FIGS. 14A and 14B illustrate electron density of the plasma formation inand around the hollow cathodes in both a bipolar hollow cathode plasmasource and a multiphase hollow cathode plasma source according toembodiments of the present invention. As the figures illustrate, forcomparable levels of electron density outside of the hollow cathodecavities, in the reaction region—as between the bipolar (FIG. 14A) andmultiphase plasma sources (FIG. 14B)—the electron density inside thehollow cathode cavities is significantly greater for the bipolar plasmasource relative to the multiphase plasma source.

FIGS. 15A and 15B illustrate ion density of the plasma formation in andaround the hollow cathodes in both a bipolar hollow cathode plasmasource and a multiphase hollow cathode plasma source according toembodiments of the present invention. As the figures illustrate, forcomparable levels of ion density outside of the hollow cathode cavities,in the reaction region—as between the bipolar (FIG. 15A) and multiphaseplasma sources (FIG. 15B)—the ion density inside the hollow cathodecavities is significantly greater for the bipolar plasma source relativeto the multiphase plasma source.

FIG. 16A illustrates ion absorption along the wall of a hollow cathodecavity in both a bipolar hollow cathode plasma source and a multiphasehollow cathode plasma source according to embodiments of the presentinvention. As the figure illustrates, the ion absorption along the wallof a hollow cathode cavity is significantly greater for the bipolarplasma source relative to the multiphase plasma source. The figure alsoillustrates that the ion absorption is at a minimum at the corners ofthe hollow cathode cavity (index values 8, 63, 89, 144). According tothe figure, the absorption rate is approximately 88% less for themultiphase arrangement compared to the bipolar arrangement (this valuewill vary depending on, for example, power levels used during operationof the plasma source).

FIG. 16B illustrates an index along a wall of a hollow cathode cavity asshown in the graph of FIG. 16A. Specifically, the values shown along thewall of the hollow cathode cavity 600 in FIG. 16B correspond to valueson the x axis of FIG. 16A (“Index along cavity wall”).

FIGS. 14-16B were generated as the results of a simulation of both abipolar hollow cathode arrangement (similar to arrangement 300) and amultiphase hollow cathode arrangement (similar to arrangement 600). Forexample, with reference to FIGS. 14A and 15A, the bipolar arrangementcomprises two linear hollow cathodes 1402 a, 1404 a (in antiphase)located in a vacuum chamber 1430. Precursor gas flows through theprecursor manifold 1410. Plasma is formed in reaction region 1420.Referring now to FIGS. 14B and 15B, the multiphase arrangement comprisesthree linear hollow cathodes 1402 b, 1404 b, 1406 b (each phase offsetfrom each other by 120°), located in a vacuum chamber 1430. Precursorgas flows through the precursor manifolds 1410. Plasma is formed inreaction region 1420. The simulation setup is further described below.Argon gas was used as the process gas in the hollow cathode cavities. Inaccordance with embodiments of the present invention, other processgasses can also be used, including without limitation Oxygen, Nitrogen,Argon, Helium, Krypton, Neon, Xenon, Hydrogen, Fluorine, Chlorine, andmixtures thereof. Reactive gasses include H2, H20, H202, N2, N02, N20,NH13, CH4, CO, CO2, SH2, other sulfur based gases, halogens, bromines,phosphorous based gases, or mixtures thereof.

Specifically, it is apparent from FIGS. 14-16B that for the same levelsof plasma density in the plasma generation region outside of the hollowcathodes between a two-phase and three-phase arrangement, the level ofwear (as indicated by plasma and ion density and ion absorption) insidethe hollow cathode cavities is significantly less for a three-phasearrangement according to embodiments of the present invention. Inembodiments of the present invention, this may lead to a longeroperational life of the hollow cathodes relative to a bipolar plasmasource. Operational life will depend on what process the plasma sourceis being used for, among other factors. For typical PECVD applicationsrelating to glass coatings, the expected operational run-lifeimprovement for a three-phase three-hollow-cathode arrangement isapproximately 60% greater as compared to the conventional bipolararrangement. In some embodiments, this may equate to approximately 200hours of additional life, for example, an operational life of 500 hoursover a baseline of 300 hours. This advantage is attributable to themultiphase power arrangement, and is not a result of merely addingadditional hollow cathodes.

The inventors have found that the amount of sputtering of the hollowcathode cavity surfaces is related to the absorption of reactive ions onthe hollow cathode cavity surfaces as determined by numericalsimulation.

The simulation software that was used for simulating gas flows and gasdischarges is a program called PIC-MC that has been developed by theFraunhofer-Institute for Surface Engineering and Thin Films IST,Braunschweig, Germany. The software combines the simulation of gasflows, magnetic fields, and plasma. For the gas flow simulation it usesthe Direct Simulation Monte Carlo (DSMC), for the magnetic fieldsimulation it uses the Boundary Element Method (BEM) and for the plasmasimulation it uses the Particle in Cell—Monte Carlo method (PIC-MC).

The simulations were made on a pseudo 2D model which is a transversal1.016 mm thick slice of the hollow cathode plasma source. Pseudo-2Dmeans that the slice has a small thickness and a periodic condition isapplied on each plane in the transversal direction.

For the simulations many different plasma forming gasses can be used; inthe previous examples argon was used. In order to limit the computationtime Si₂H₆ was chosen as coating precursor and among its possiblereactions the following two were selected:Si₂H₆ +e ⁻→Si₂H₄ ⁺+2H+2e ⁻  (2)Si₂H₆ +e ⁻→SiH₃+SiH₂+H+e ⁻  (2)

Hydrogen species were not included in the simulations.

For each given set of input parameters the simulation yields dataregarding number and velocity of the different gas phase species (atoms,ions, molecules and electrons) throughout the space they occupy. Fromthis data certain values can be calculated, such as densities andfluxes, where a flux is the rate of movement of gas phase species acrossa unit area (unit: mol·m⁻²·s⁻¹).

Another useful calculation is the flux that is absorbed on a certainsurface. Given a certain sticking coefficient of the cathode cavitymaterial, the ion absorption on its surface can be calculated from theion flux directed at it. By correlating results from the operation ofbipolar hollow cathodes with simulation data the inventors found thatthe formation of debris and thus the cavity surface sputtering observedon real plasma sources was related to the level of ionized plasmaspecies absorbed by the hollow cathodes' cavity surfaces according tothe simulation model.

Argon absorption is an easily derived property from the plasmasimulation that was used. Further, argon absorption is an effectivegauge of the ion energy and particle flux that is incident to theelectrode surface. Those skilled in the art will understand that the ionenergy and particle flux are the major driving factors behind thephysical process of sputtering or electrode erosion. Debris generationoccurs when the balance of sputter rate versus deposition of sputteredmaterial from nearby surfaces is biased toward a net deposition. Thiseffect can be observed in FIGS. 16A and 16B, which indicate reducedsputtering and net deposition in the corners of the rectangularelectrodes, where ion absorption was found (through simulation) to belowest.

Accordingly, although the actual sputtering value is not measured by thesimulation, the inventors have used the argon absorption values as anindicator of the sputtering or electrode erosion from the multiphaseembodiment described here.

Low levels of ionized plasma species absorbed by the hollow cathodes'cavity surfaces mean that the level of cavity sputtering is low anddebris formation is low. As shown in FIGS. 16A and 16B, the bipolarplasma source resulted in increased sputtering and wear of the majorityof the electrode surface, where both the bipolar and multiphase plasmasources had equal plasma energy in the process chamber. The additionalsputtered material from the bipolar plasma source can also result inincreased debris when it is deposited on surfaces which are notundergoing intense sputtering, such as the corners of the electrodecavities and surfaces external to the plasma source (which are atfloating or ground potential and not subject to sputtering). The natureand amount of this debris will be heavily dependent upon the combinationof electrode surface material and plasma gas.

Another important quantity is the electron density generated. Theelectron density has a major influence on surface treatment or coatingefficiency, with high electron densities leading to high surfacetreatment or coating efficiencies. In the present simulations theelectron density was determined in the vacuum chamber on a line set at adistance of 2.54 mm from the chamber structure that supports the plasmasource and averaged.

The inventors surprisingly found that the level of ionized plasmaspecies absorbed by the cathode cavity surfaces was reduced when threehollow cathodes were used each with a phase shift of 120 degrees ascompared to a configuration with two hollow cathodes with a phase shiftof 180 degrees.

According to this embodiment of the present invention, the inventorssurprisingly found that the intensity of electron density in a reactionregion outside the hollow cathodes was similar for both a three-phase,three-hollow-cathode arrangement and a two-phase, two-hollow-cathodearrangement. This is surprising because, for example, the three-phase,three-hollow-cathode arrangement produces plasma concentrated on alarger area and experiences less wear inside the hollow cathodes thanthe two-phase, two-hollow cathode arrangement.

Many other combinations of hollow cathodes and multiphase power inputsare possible with the specific arrangements being designed to suit aparticular application, as one of ordinary skill in the art willappreciate from the present disclosure.

While various embodiments have been described above, it should beunderstood that they have been presented by way of example only, and notlimitation. Thus, the breadth and scope of the present disclosure shouldnot limited by any of the above-described exemplary embodiments.Moreover, any combination of the above-described elements in allpossible variations thereof is encompassed by the disclosure unlessotherwise indicated herein or otherwise clearly contradicted by context.

Additionally, while the processes described above and illustrated in thedrawings are shown as a sequence of steps, this was done solely for thesake of illustration. Accordingly, it is contemplated that some stepsmay be added, some steps may be omitted, the order of the steps may berearranged, and some steps may be performed in parallel.

What is claimed is:
 1. A method of producing a plasma comprising:providing at least three hollow cathodes, including a first hollowcathode, a second hollow cathode, and a third hollow cathode, eachhollow cathode having a plasma exit region; and providing a source ofpower capable of producing multiple output waves, including a firstoutput wave, a second output wave, and a third output wave, wherein thefirst output wave and the second output wave are out of phase, thesecond output wave and the third output wave are out of phase, and thefirst output wave and the third output wave are out of phase; whereineach hollow cathode is electrically connected to the source of powersuch that the first hollow cathode is electrically connected to thefirst output wave, the second hollow cathode is electrically connectedto the second output wave, and the third hollow cathode is electricallyconnected to the third output wave; wherein electrical current flowsbetween the at least three hollow cathodes that are out of electricalphase; wherein each hollow cathode alternately serves as anode andcathode when powered by the multiple output waves and wherein a plasmais generated between the hollow cathodes.
 2. The method of claim 1,wherein the plasma includes active electron emission for at leastsubstantially 80% of a period of the multiple output waves.
 3. Themethod of claim 1, wherein the plasma includes active electron emissionfor at least substantially 90% of a period of the multiple output waves.4. The method of claim 1, wherein the plasma includes active electronemission for substantially 100% of a period of the multiple outputwaves.
 5. The method of claim 1, wherein the at least three hollowcathodes are out of electrical phase by a phase angle different from180°.
 6. The method of claim 1, wherein the at least three hollowcathodes are out of electrical phase by a phase angle of 120°.
 7. Themethod of claim 1, wherein each adjacent pair of the at least threehollow cathodes is out of electrical phase by the same phase angle aseach other adjacent pair of the at least three hollow cathodes.
 8. Themethod of claim 1, wherein the at least three hollow cathodes are linearhollow cathodes.
 9. The method of claim 1, wherein the at least threehollow cathodes each include elongated cavities.
 10. The method of claim1, wherein the plasma exit region for each of the at least three hollowcathodes includes a plurality of plasma exit orifices.
 11. The method ofclaim 1, wherein the plasma exit region for each of the at least threehollow cathodes includes a plasma exit slot.
 12. The method of claim 1,wherein the at least three hollow cathodes are each electricallyinsulated such that only interior surfaces of the hollow cathode and theplasma exit region are electron-emitting and -accepting.
 13. The methodof claim 1, wherein virtually all the generated plasma flows through theplasma exit region of each of the at least three hollow cathodes. 14.The method of claim 1, wherein current flow is comprised of electronsderived from secondary electron emission.
 15. The method of claim 1,wherein the current flow is comprised of electrons derived fromthermionic-emitted electrons.
 16. The method of claim 1, wherein the atleast three hollow cathodes are linearly arranged.
 17. The method ofclaim 1, wherein the at least three hollow cathodes are configured todirect each of the plasma exit regions to a common line.
 18. The methodof claim 1, wherein a distance between each pair of the at least threehollow cathodes is the same distance.
 19. The method of claim 1, whereinthe electrical current flowing between the at least three hollowcathodes that are out of electrical phase is a result of an electricpotential difference between the at least three hollow cathodes.
 20. Themethod of claim 19, wherein the electric potential difference is atleast 50V between any two of the at least three hollow cathodes.
 21. Themethod of claim 19, wherein the electric potential difference is atleast 200V between any two of the at least three hollow cathodes. 22.The method of claim 1, wherein the multiple output waves comprise squarewaves whereby the electric potential difference is reduced relative tosinusoidal waves for the same overall power input.
 23. The method ofclaim 1, wherein the source of power is in the form of AC electricalenergy.
 24. The method of claim 1, wherein the source of power is in theform of pulsed electrical energy.
 25. The method of claim 1, wherein thecontinuously generated plasma is substantially uniform over its lengthin the substantial absence of magnetic-field driven closed circuitelectron drift.
 26. The method of claim 1, wherein the plasma is madesubstantially uniform over its length from about 0.1 m to about 1 m. 27.The method of claim 1, wherein the plasma is made substantially uniformover its length from about 1 m to about 4 m.
 28. The method of claim 1,wherein the frequencies of each of the multiple output waves are equaland are in the range from about 1 kHz to about 500 MHz.
 29. The methodof claim 1, wherein the frequencies of each of the multiple output wavesare equal and are in the range from about 1 kHz to about 1 MHz.
 30. Themethod of claim 1, wherein the frequencies of each of the multipleoutput waves are equal and are in the range from about 10 kHz to about200 kHz.
 31. The method of claim 1, wherein the frequencies of each ofthe multiple output waves are equal and are in the range from about 20kHz to about 100 kHz.
 32. The method of claim 1, wherein the electronsfrom an emitting surface are confined by the hollow cathode effect. 33.The method of claim 1, wherein the electrons from an emitting surface ofeach of the at least three hollow cathodes are not confined by magneticfields.
 34. The method of claim 1, wherein at least one of the multipleoutput waves produced by the source of power is configured to power aplurality of the at least three hollow cathodes.
 35. The method of claim1, further comprising: providing a substrate; forming a coating on thesubstrate using plasma-enhanced chemical vapor deposition.